The gastrocnemius is the more superficial muscle of the two muscles that make up the calves. This means that it is the one that is more visible when a person is wearing shorts. The soleus runs underneath the gastrocnemius. The gastrocnemius is the more active of the two muscles when the leg is fully extended or straight, because it is the longer muscle. The soleus is relatively less active when doing standing calve raises or any type of calve raise where the leg is fully extended. The way to target the soleus is simple, have the knees in a bent position. The gastrocnemius will be relatively relaxed when the leg is flexed or shortened due to the shortened position it is in. So, the simple formula is standing calve raises to target the gastrocnemius and seated calve raises to target the soleus.
The calves are a thick, dense muscle made up of both fast and slow twitch fibers. They are constantly in use with everyday walking around. They can handle a fairly high training volume for being a small muscle group. That being said, they should be given ample rest between training sessions. As a generalization, the soleus is composed of a higher percentage of slow twitch muscle fibers compared to the gastrocnemius, which has a higher percentage of fast twitch fibers. It would be wise to train to these characteristics and perform in the 8-12 rep range for the gastrocnemius and anywhere from 20-50 for the soleus, with little rest between sets. These ranges and training methods are not the golden rule, just a guide as to where to start. Learn to read what your calve muscles respond to and ride it out until the response is minimized, at which time, switch it up and provide the muscle with a new stress.